In [1]:
#importing the libraries
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_samples,silhouette_score

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import matplotlib.cm as cm 
import seaborn as sns
In [2]:
#importing the libraries
from sklearn.decomposition import PCA

#To perform hierarchical clustering
from scipy.cluster.hierarchy import linkage
from scipy.cluster.hierarchy import dendrogram
from scipy.cluster.hierarchy import cut_tree
In [3]:
#reading csv file as df
df=pd.read_csv('C:\\Users\\MERINA ANGEL\\Downloads\\Country-data.csv')
In [4]:
df #printing df
Out[4]:
country child_mort exports health imports income inflation life_expec total_fer gdpp
0 Afghanistan 90.2 10.0 7.58 44.9 1610 9.44 56.2 5.82 553
1 Albania 16.6 28.0 6.55 48.6 9930 4.49 76.3 1.65 4090
2 Algeria 27.3 38.4 4.17 31.4 12900 16.10 76.5 2.89 4460
3 Angola 119.0 62.3 2.85 42.9 5900 22.40 60.1 6.16 3530
4 Antigua and Barbuda 10.3 45.5 6.03 58.9 19100 1.44 76.8 2.13 12200
... ... ... ... ... ... ... ... ... ... ...
162 Vanuatu 29.2 46.6 5.25 52.7 2950 2.62 63.0 3.50 2970
163 Venezuela 17.1 28.5 4.91 17.6 16500 45.90 75.4 2.47 13500
164 Vietnam 23.3 72.0 6.84 80.2 4490 12.10 73.1 1.95 1310
165 Yemen 56.3 30.0 5.18 34.4 4480 23.60 67.5 4.67 1310
166 Zambia 83.1 37.0 5.89 30.9 3280 14.00 52.0 5.40 1460

167 rows × 10 columns

In [5]:
df.head() #printing first 5 rows
Out[5]:
country child_mort exports health imports income inflation life_expec total_fer gdpp
0 Afghanistan 90.2 10.0 7.58 44.9 1610 9.44 56.2 5.82 553
1 Albania 16.6 28.0 6.55 48.6 9930 4.49 76.3 1.65 4090
2 Algeria 27.3 38.4 4.17 31.4 12900 16.10 76.5 2.89 4460
3 Angola 119.0 62.3 2.85 42.9 5900 22.40 60.1 6.16 3530
4 Antigua and Barbuda 10.3 45.5 6.03 58.9 19100 1.44 76.8 2.13 12200

the export, import, health are in percentage format converting them to actual values

In [6]:
df['exports'] = df['exports']*df['gdpp']/100
df['imports'] = df['imports']*df['gdpp']/100
df['health'] = df['health']*df['gdpp']/100
In [7]:
df.isnull().sum() #printing null values
Out[7]:
country       0
child_mort    0
exports       0
health        0
imports       0
income        0
inflation     0
life_expec    0
total_fer     0
gdpp          0
dtype: int64
In [8]:
#5 point summary of numerical columns
df.describe()
Out[8]:
child_mort exports health imports income inflation life_expec total_fer gdpp
count 167.000000 167.000000 167.000000 167.000000 167.000000 167.000000 167.000000 167.000000 167.000000
mean 38.270060 7420.618847 1056.733204 6588.352108 17144.688623 7.781832 70.555689 2.947964 12964.155689
std 40.328931 17973.885795 1801.408906 14710.810418 19278.067698 10.570704 8.893172 1.513848 18328.704809
min 2.600000 1.076920 12.821200 0.651092 609.000000 -4.210000 32.100000 1.150000 231.000000
25% 8.250000 447.140000 78.535500 640.215000 3355.000000 1.810000 65.300000 1.795000 1330.000000
50% 19.300000 1777.440000 321.886000 2045.580000 9960.000000 5.390000 73.100000 2.410000 4660.000000
75% 62.100000 7278.000000 976.940000 7719.600000 22800.000000 10.750000 76.800000 3.880000 14050.000000
max 208.000000 183750.000000 8663.600000 149100.000000 125000.000000 104.000000 82.800000 7.490000 105000.000000
In [9]:
#percentile values for numerical columns
df.describe(percentiles=[.25,.50,.75,.100])
Out[9]:
child_mort exports health imports income inflation life_expec total_fer gdpp
count 167.000000 167.000000 167.000000 167.000000 167.000000 167.000000 167.000000 167.000000 167.000000
mean 38.270060 7420.618847 1056.733204 6588.352108 17144.688623 7.781832 70.555689 2.947964 12964.155689
std 40.328931 17973.885795 1801.408906 14710.810418 19278.067698 10.570704 8.893172 1.513848 18328.704809
min 2.600000 1.076920 12.821200 0.651092 609.000000 -4.210000 32.100000 1.150000 231.000000
10% 4.200000 110.224800 36.502560 211.005600 1524.000000 0.587800 57.820000 1.452000 593.800000
25% 8.250000 447.140000 78.535500 640.215000 3355.000000 1.810000 65.300000 1.795000 1330.000000
50% 19.300000 1777.440000 321.886000 2045.580000 9960.000000 5.390000 73.100000 2.410000 4660.000000
75% 62.100000 7278.000000 976.940000 7719.600000 22800.000000 10.750000 76.800000 3.880000 14050.000000
max 208.000000 183750.000000 8663.600000 149100.000000 125000.000000 104.000000 82.800000 7.490000 105000.000000
In [10]:
#printing the information of non null values
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 167 entries, 0 to 166
Data columns (total 10 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   country     167 non-null    object 
 1   child_mort  167 non-null    float64
 2   exports     167 non-null    float64
 3   health      167 non-null    float64
 4   imports     167 non-null    float64
 5   income      167 non-null    int64  
 6   inflation   167 non-null    float64
 7   life_expec  167 non-null    float64
 8   total_fer   167 non-null    float64
 9   gdpp        167 non-null    int64  
dtypes: float64(7), int64(2), object(1)
memory usage: 13.2+ KB

data visualization¶

In [11]:
fig, ax = plt.subplots(figsize=(10,10)) 
sns.heatmap(df.corr(),annot=True) #visualizing the correlation
Out[11]:
<AxesSubplot:>
In [12]:
#visualizing the graph of all numeric columns correlation at on shot
sns.pairplot(df)
Out[12]:
<seaborn.axisgrid.PairGrid at 0x21d957e4190>
In [13]:
#scatterplot says relation betweeen 2 variables
plt.figure(figsize = (18, 5))
plt.scatter(x='income',y='child_mort',data=df)
Out[13]:
<matplotlib.collections.PathCollection at 0x21d9c5c0370>
In [14]:
#scatterplot says relation betweeen 2 variables
plt.figure(figsize = (18, 5))
plt.scatter(x='inflation',y='life_expec',data=df)
Out[14]:
<matplotlib.collections.PathCollection at 0x21d9c62eda0>
In [15]:
#histplot draws histogram for given variable with frequency
plt.hist(df['inflation'],5,histtype='bar',edgecolor='black',color='g')
plt.xlabel('inflation')
plt.ylabel('freq')
plt.show()
In [16]:
df.columns=df.columns
#df.columns are assigned
In [17]:
df.columns#printing columns of df
Out[17]:
Index(['country', 'child_mort', 'exports', 'health', 'imports', 'income',
       'inflation', 'life_expec', 'total_fer', 'gdpp'],
      dtype='object')
In [18]:
fig=plt.subplots(figsize=(10,15))
for i,feature in enumerate(df.drop('country',axis=1).columns):
    plt.subplot(6,3,i+1)
    plt.subplots_adjust(hspace=2.0)
    sns.distplot(df[feature])
    plt.tight_layout()
    #checking dist plot for numeric features

C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
In [19]:
#checking outliers of all independent columns
j=1
plt.figure(figsize=(20,40))
col=['child_mort', 'exports', 'health', 'imports', 'income',
       'inflation', 'life_expec', 'total_fer', 'gdpp']
for i in col:
    plt.subplot(len(col)+1,2,j)
    sns.boxplot(df[i])
    plt.title(i,color='white')
    j=j+1
    #visualizing boxplot for numeric columns which represents the outliers of that particular column

C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

EDA¶

In [ ]:
In [20]:
Q1=df.quantile(0.25)
Q3=df.quantile(0.75)
IQR=Q3-Q1
#quartile 1 quartile 3 values of df columns
In [21]:
Q1 #printing Q1 values of df columns
Out[21]:
child_mort       8.2500
exports        447.1400
health          78.5355
imports        640.2150
income        3355.0000
inflation        1.8100
life_expec      65.3000
total_fer        1.7950
gdpp          1330.0000
Name: 0.25, dtype: float64
In [22]:
Q3#printing Q1 values of df columns
Out[22]:
child_mort       62.10
exports        7278.00
health          976.94
imports        7719.60
income        22800.00
inflation        10.75
life_expec       76.80
total_fer         3.88
gdpp          14050.00
Name: 0.75, dtype: float64
In [23]:
IQR #inter quartile range of df columns
Out[23]:
child_mort       53.8500
exports        6830.8600
health          898.4045
imports        7079.3850
income        19445.0000
inflation         8.9400
life_expec       11.5000
total_fer         2.0850
gdpp          12720.0000
dtype: float64
In [24]:
df.mean() #mean of df columns

C:\Users\MERINA ANGEL\AppData\Local\Temp\ipykernel_9392\499045928.py:1: FutureWarning: Dropping of nuisance columns in DataFrame reductions (with 'numeric_only=None') is deprecated; in a future version this will raise TypeError.  Select only valid columns before calling the reduction.
  df.mean() #mean of df columns
Out[24]:
child_mort       38.270060
exports        7420.618847
health         1056.733204
imports        6588.352108
income        17144.688623
inflation         7.781832
life_expec       70.555689
total_fer         2.947964
gdpp          12964.155689
dtype: float64
In [25]:
df1=df.drop('country',axis=1) #dropping country column from df and assigning it to df1 variable
In [26]:
#removing outliers by replacing them eith mean 
for i in df1.columns:
    q1 , q3 =df1[i].quantile([0.25,0.75]) 
    iqr = q3-q1
    lf , uf = q1-1.5*iqr , q3+1.5*iqr
    df1[i] = np.where(df1[i] <lf ,df1[i].mean(),df1[i])
    df1[i] = np.where(df1[i] >uf ,df1[i].mean(),df1[i])
    
    
    #replacing the outliers with mean, which is beyond lower fence and upper fence
In [27]:
#checking outliers of all independent columns
j=1
plt.figure(figsize=(20,40))
col=['child_mort', 'exports', 'health', 'imports', 'income',
       'inflation', 'life_expec', 'total_fer', 'gdpp']
for i in col:
    plt.subplot(len(col)+1,2,j)
    sns.boxplot(df1[i])
    plt.title(i,color='white')
    j=j+1
    #checking outliers using boxplot 

C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
In [28]:
y=df['country']
In [29]:
y#printing y (i.e country column)
Out[29]:
0              Afghanistan
1                  Albania
2                  Algeria
3                   Angola
4      Antigua and Barbuda
              ...         
162                Vanuatu
163              Venezuela
164                Vietnam
165                  Yemen
166                 Zambia
Name: country, Length: 167, dtype: object
In [30]:
#standardising the df1 variable
from sklearn.preprocessing import StandardScaler

scaler= StandardScaler() #assigning standardscalar to scalar variable

scaled_features= scaler.fit_transform(df1)
In [31]:
#importing libraries
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
In [ ]:

PCA¶

PCA means reducing the dimensionality of data.

In [32]:
from sklearn.decomposition import PCA #importing pca
pca = PCA()
X_pca = pca.fit_transform(scaled_features) #fitting and transforming the standardized data using pca

#visualizing the explained variance ratio
plt.figure()
plt.plot(np.cumsum(pca.explained_variance_ratio_))
plt.xlabel('Number of Components')
plt.ylabel('Variance (%)') #for each component
plt.title('Explained Variance')
plt.grid() #formation of grid for graph
plt.show()

# Create principal components
pca = PCA(n_components=3) #3 features covers 97% of data
X_pca = pca.fit_transform(scaled_features)

# Convert to dataframe
component_names = [f"PC{i+1}" for i in range(X_pca.shape[1])] #formation of features
X_pca = pd.DataFrame(X_pca, columns=component_names)#creating dataframe for those pc features

X_pca.head() #printing 5 rows
Out[32]:
PC1 PC2 PC3
0 -3.531169 1.338167 -0.315297
1 -0.106481 -1.614102 -0.209965
2 -0.779823 -0.790575 1.601960
3 -3.490239 2.389875 1.763175
4 1.818064 -0.239527 -0.519753
In [33]:
# Show dataframe sorted by PC2
idx = X_pca["PC2"].sort_values(ascending=False).index
cols = df1.columns
df1.loc[idx, cols]
Out[33]:
child_mort exports health imports income inflation life_expec total_fer gdpp
49 111.0 14671.800 766.0800 10071.900 33700.0 7.781832 60.9 5.21 17100.0
3 119.0 2199.190 100.6050 1514.370 5900.0 22.400000 60.1 6.16 3530.0
42 3.6 15461.600 1838.7600 17710.000 33900.0 2.010000 79.9 1.42 30800.0
37 116.0 137.274 26.4194 165.664 609.0 20.800000 57.5 6.54 334.0
97 137.0 161.424 35.2584 248.508 1870.0 4.370000 59.5 6.55 708.0
... ... ... ... ... ... ... ... ... ...
34 15.7 1199.280 231.1920 1030.560 9530.0 6.940000 74.6 1.59 4560.0
6 18.1 669.760 141.6800 1458.660 6700.0 7.770000 73.3 1.69 3220.0
1 16.6 1145.200 267.8950 1987.740 9930.0 4.490000 76.3 1.65 4090.0
102 17.2 638.960 190.7100 1279.550 3910.0 11.100000 69.7 1.27 1630.0
20 6.9 1369.170 511.7100 2364.930 9720.0 1.400000 76.8 1.31 4610.0

167 rows × 9 columns

In [34]:
explained_variance=pca.explained_variance_ratio_
explained_variance #explained variance ratio
Out[34]:
array([0.68858675, 0.11663566, 0.09176812])
In [35]:
with plt.style.context('dark_background'):
    plt.figure(figsize=(6, 4))

    plt.bar(range(3), explained_variance, alpha=0.5, align='center',
            label='individual explained variance')
    plt.ylabel('Explained variance ratio')
    plt.xlabel('Principal components')
    plt.legend(loc='best')
    plt.tight_layout()
#explained variance ratio vs pc
In [36]:
fig = plt.figure(figsize = (12,8))
sns.boxplot(data=X_pca)
plt.show()
#printing boxplot for pc features

After implementing pca and doing kmeans and hierarchical will help to increase the accuracy of kmeans and hierarchical models

k means¶

In [37]:
#elbow method==> this helps in knowing how many clusters to be formed
cs = []
for i in range(1, 11):
    kmeans = KMeans(n_clusters = i, init = 'k-means++', max_iter = 600, n_init = 10, random_state = 7)
    
    kmeans.fit(X_pca)
    
    cs.append(kmeans.inertia_)

# plot the elbow method graph for knowing number of clusters
plt.plot(range(1, 11), cs)
plt.title('The Elbow Method')
plt.xlabel('Number of clusters')
plt.ylabel('Inertia')
plt.show()
In [38]:
# Calculate Silhoutte Score
import sklearn
score = sklearn.metrics.silhouette_score(X_pca, kmeans.labels_, metric='euclidean')
#
# Print the score
#
print('Silhouetter Score: %.3f' % score)

Silhouetter Score: 0.341
In [39]:
# finding silhouette score for different clusters values
for i in range(2,10):
    k_means = KMeans(n_clusters=i, max_iter = 300, init = 'k-means++',random_state = 0,n_init = 10)
    cluster_labels=k_means.fit_predict(X_pca)
    print(silhouette_score(X_pca, cluster_labels))

0.4915156341368341
0.4523045687796382
0.3641800740755204
0.3695124251485627
0.33305771186163985
0.3526874298480885
0.3559790764532396
0.36533891313915906
In [40]:
from sklearn.metrics import silhouette_score
sse_ = []
for k in range(2, 10):
    kmeans = KMeans(n_clusters=k).fit(X_pca)
    sse_.append([k, silhouette_score(X_pca, kmeans.labels_)])
    
plt.plot(pd.DataFrame(sse_)[0], pd.DataFrame(sse_)[1])
plt.show()
#silhouette score graph
In [41]:
ssd = [] # An empty list for sum of squared distances to be appended for k values 2 to 10

for k in range(2,11):
    model = KMeans(n_clusters=k)
    model.fit(X_pca)
    ssd.append(model.inertia_)
    # model.inertia_: Sum of squared distances of samples to their closest cluster center, weighted by the sample weights if provided 
    # (from documentation - https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html)
In [54]:
model = KMeans(n_clusters=3) #no. of clusters= 3
model.fit(scaled_features)

k_means_labels = model.fit_predict(X_pca)
k_means_labels
Out[54]:
array([2, 1, 1, 2, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 2, 1, 1, 1, 1,
       1, 0, 1, 2, 2, 1, 2, 0, 1, 2, 2, 0, 1, 1, 2, 2, 2, 1, 2, 0, 0, 0,
       0, 1, 1, 1, 1, 0, 2, 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 1, 1, 2, 2, 1,
       1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 2, 2, 0, 1, 2, 0, 1, 2,
       2, 0, 0, 0, 1, 2, 2, 0, 1, 2, 0, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1,
       0, 0, 2, 2, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 0, 2, 1, 0,
       2, 0, 0, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 2, 1, 2, 2, 1, 1, 1,
       1, 2, 1, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2])
In [55]:
model.inertia_ #inertia -->it should be minimum as much as possible
Out[55]:
344.4151750150594
In [56]:
range_n_clusters=[1,2,3,4,5,6,7,8,9,10]
In [57]:
# visualizing the silhouette score scatter plots of cluster data
X=X_pca
import matplotlib.cm as cm 

range_n_clusters = [2,3,4,6,8,10, 14,17, 19,22,24,26,27]
for n_clusters in range_n_clusters:
    # Create a subplot with 1 row and 2 columns
    fig, (ax1, ax2) = plt.subplots(1, 2)
    fig.set_size_inches(18, 7)

    # The 1st subplot is the silhouette plot
    # The silhouette coefficient can range from -1, 1 but in this example all
    # lie within [-0.1, 1]
    ax1.set_xlim([-0.1, 1])
    # The (n_clusters+1)*10 is for inserting blank space between silhouette
    # plots of individual clusters, to demarcate them clearly.
    ax1.set_ylim([0, len(X_pca) + (n_clusters + 1) * 10])

    # Initialize the clusterer with n_clusters value and a random generator
    # seed of 10 for reproducibility.
    clusterer = KMeans(n_clusters=n_clusters, random_state=10)
    cluster_labels = clusterer.fit_predict(X_pca)

    # The silhouette_score gives the average value for all the samples.
    # This gives a perspective into the density and separation of the formed
    # clusters
    silhouette_avg = silhouette_score(X_pca, cluster_labels)
    print("For n_clusters =", n_clusters,
          "The average silhouette_score is :", silhouette_avg)

    # Compute the silhouette scores for each sample
    sample_silhouette_values = silhouette_samples(X_pca, cluster_labels)

    y_lower = 10
    for i in range(n_clusters):
        # Aggregate the silhouette scores for samples belonging to
        # cluster i, and sort them
        ith_cluster_silhouette_values = \
            sample_silhouette_values[cluster_labels == i]

        ith_cluster_silhouette_values.sort()

        size_cluster_i = ith_cluster_silhouette_values.shape[0]
        y_upper = y_lower + size_cluster_i

        color = cm.nipy_spectral(float(i) / n_clusters)
        ax1.fill_betweenx(np.arange(y_lower, y_upper),
                          0, ith_cluster_silhouette_values,
                          facecolor=color, edgecolor=color, alpha=0.7)

        # Label the silhouette plots with their cluster numbers at the middle
        ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))

        # Compute the new y_lower for next plot
        y_lower = y_upper + 10  # 10 for the 0 samples

    ax1.set_title("The silhouette plot for the various clusters.")
    ax1.set_xlabel("The silhouette coefficient values")
    ax1.set_ylabel("Cluster label")

    # The vertical line for average silhouette score of all the values
    ax1.axvline(x=silhouette_avg, color="red", linestyle="--")

    ax1.set_yticks([])  # Clear the yaxis labels / ticks
    ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])

    # 2nd Plot showing the actual clusters formed
    colors = cm.nipy_spectral(cluster_labels.astype(float) / n_clusters)
    ax2.scatter(X_pca['PC1'],X_pca['PC2'], marker='.', s=30, lw=0, alpha=0.7,
                c=colors, edgecolor='k')

    # Labeling the clusters
    centers = clusterer.cluster_centers_
    # Draw white circles at cluster centers
    ax2.scatter(centers[:,0], centers[:, 1], marker='o',
                c="white", alpha=1, s=200, edgecolor='k')

    for i, c in enumerate(centers):
        ax2.scatter(c[0], c[1], marker='$%d$' % i, alpha=1,
                    s=50, edgecolor='k')

    ax2.set_title("The visualization of the clustered data.")
    ax2.set_xlabel("Feature space for the 1st feature")
    ax2.set_ylabel("Feature space for the 2nd feature")

    plt.suptitle(("Silhouette analysis for KMeans clustering on sample data "
                  "with n_clusters = %d" % n_clusters),
                 fontsize=14, fontweight='bold')

plt.show()

For n_clusters = 2 The average silhouette_score is : 0.4915156341368341
For n_clusters = 3 The average silhouette_score is : 0.4523045687796382
For n_clusters = 4 The average silhouette_score is : 0.3661167171483697
For n_clusters = 6 The average silhouette_score is : 0.3254753340986423
For n_clusters = 8 The average silhouette_score is : 0.36039184694500537
For n_clusters = 10 The average silhouette_score is : 0.3423113217517925
For n_clusters = 14 The average silhouette_score is : 0.32165240875961587
For n_clusters = 17 The average silhouette_score is : 0.3321096817074923
For n_clusters = 19 The average silhouette_score is : 0.3405701437336835
For n_clusters = 22 The average silhouette_score is : 0.3386941589882622
For n_clusters = 24 The average silhouette_score is : 0.3469983497144465
For n_clusters = 26 The average silhouette_score is : 0.32075268466246293
For n_clusters = 27 The average silhouette_score is : 0.34165030762715365

selecting 3 clusters as k.As it have less outliers in above graph, which can be taken as perfect clusters for given data.¶

so we can say that we will use pca with kmeans to form cluster by reducing the dimensions and cluster = 2,3,4 can be taken and mostly it is better to take 3 in this business case¶

In [58]:
# concatinating the clustering labels with dataframe
country_df_clustered = df.iloc[:,:]
country_df_clustered = pd.concat([df, pd.DataFrame(k_means_labels, columns=['cluster_id_km'])], axis = 1)
country_df_clustered.head()
Out[58]:
country child_mort exports health imports income inflation life_expec total_fer gdpp cluster_id_km
0 Afghanistan 90.2 55.30 41.9174 248.297 1610 9.44 56.2 5.82 553 2
1 Albania 16.6 1145.20 267.8950 1987.740 9930 4.49 76.3 1.65 4090 1
2 Algeria 27.3 1712.64 185.9820 1400.440 12900 16.10 76.5 2.89 4460 1
3 Angola 119.0 2199.19 100.6050 1514.370 5900 22.40 60.1 6.16 3530 2
4 Antigua and Barbuda 10.3 5551.00 735.6600 7185.800 19100 1.44 76.8 2.13 12200 0
In [59]:
#df2=pd.DataFrame(k_means_labels)
In [60]:
#df2.value_counts() #checking value counts
In [61]:
#cluster formation based on country 
print("Cluster 0 of K_means Clustering model : ")
print(country_df_clustered[country_df_clustered['cluster_id_km'] == 0].country.unique())
print('\n')

print("Cluster 1 of K_means Clustering model : ")
print(country_df_clustered[country_df_clustered['cluster_id_km'] == 1].country.unique())
print('\n')


print("Cluster 2 of K_means Clustering model : ")
print(country_df_clustered[country_df_clustered['cluster_id_km'] == 2].country.unique())
print('\n')

Cluster 0 of K_means Clustering model : 
['Antigua and Barbuda' 'Australia' 'Austria' 'Bahamas' 'Bahrain'
 'Barbados' 'Belgium' 'Brunei' 'Canada' 'Chile' 'Croatia' 'Cyprus'
 'Czech Republic' 'Denmark' 'Equatorial Guinea' 'Estonia' 'Finland'
 'France' 'Germany' 'Greece' 'Hungary' 'Iceland' 'Ireland' 'Israel'
 'Italy' 'Japan' 'Kuwait' 'Latvia' 'Libya' 'Lithuania' 'Luxembourg'
 'Malaysia' 'Malta' 'Netherlands' 'New Zealand' 'Norway' 'Oman' 'Poland'
 'Portugal' 'Qatar' 'Saudi Arabia' 'Seychelles' 'Singapore'
 'Slovak Republic' 'Slovenia' 'South Korea' 'Spain' 'Sweden' 'Switzerland'
 'United Arab Emirates' 'United Kingdom' 'United States']


Cluster 1 of K_means Clustering model : 
['Albania' 'Algeria' 'Argentina' 'Armenia' 'Azerbaijan' 'Bangladesh'
 'Belarus' 'Belize' 'Bhutan' 'Bolivia' 'Bosnia and Herzegovina' 'Botswana'
 'Brazil' 'Bulgaria' 'Cambodia' 'Cape Verde' 'China' 'Colombia'
 'Costa Rica' 'Dominican Republic' 'Ecuador' 'Egypt' 'El Salvador' 'Fiji'
 'Georgia' 'Grenada' 'Guatemala' 'Guyana' 'Haiti' 'India' 'Indonesia'
 'Iran' 'Iraq' 'Jamaica' 'Jordan' 'Kazakhstan' 'Kyrgyz Republic' 'Lebanon'
 'Macedonia, FYR' 'Maldives' 'Mauritius' 'Micronesia, Fed. Sts.' 'Moldova'
 'Mongolia' 'Montenegro' 'Morocco' 'Myanmar' 'Nepal' 'Panama' 'Paraguay'
 'Peru' 'Philippines' 'Romania' 'Russia' 'Samoa' 'Serbia' 'South Africa'
 'Sri Lanka' 'St. Vincent and the Grenadines' 'Suriname' 'Tajikistan'
 'Thailand' 'Tonga' 'Tunisia' 'Turkey' 'Turkmenistan' 'Ukraine' 'Uruguay'
 'Uzbekistan' 'Vanuatu' 'Venezuela' 'Vietnam']


Cluster 2 of K_means Clustering model : 
['Afghanistan' 'Angola' 'Benin' 'Burkina Faso' 'Burundi' 'Cameroon'
 'Central African Republic' 'Chad' 'Comoros' 'Congo, Dem. Rep.'
 'Congo, Rep.' "Cote d'Ivoire" 'Eritrea' 'Gabon' 'Gambia' 'Ghana' 'Guinea'
 'Guinea-Bissau' 'Kenya' 'Kiribati' 'Lao' 'Lesotho' 'Liberia' 'Madagascar'
 'Malawi' 'Mali' 'Mauritania' 'Mozambique' 'Namibia' 'Niger' 'Nigeria'
 'Pakistan' 'Rwanda' 'Senegal' 'Sierra Leone' 'Solomon Islands' 'Sudan'
 'Tanzania' 'Timor-Leste' 'Togo' 'Uganda' 'Yemen' 'Zambia']

HIERARCHICAL CLUSTERING¶

In [62]:
#Finding the optimal number of clusters using the dendrogram  
import scipy.cluster.hierarchy as shc  
dendro = shc.dendrogram(shc.linkage(scaled_features, method="ward"))  
plt.title("Dendrogrma Plot")  
plt.ylabel("Euclidean Distances")  
plt.xlabel("Customers")  
plt.show()
In [63]:
#Finding the optimal number of clusters using the dendrogram  
import scipy.cluster.hierarchy as shc  
dendro = shc.dendrogram(shc.linkage(X_pca, method="ward"))  
plt.title("Dendrogrma Plot")  
plt.ylabel("Euclidean Distances")  
plt.xlabel("Customers")  
plt.show()

another way of hierarchical clustering representation¶

In [64]:
from sklearn.cluster import AgglomerativeClustering
model = AgglomerativeClustering(n_clusters=None,distance_threshold=0) # each point starts as its own cluster
# From sklearn documentation: 
# distance_thresholdfloat, default=None
# The linkage distance threshold above which, clusters will not be merged. If not None, n_clusters must be None and compute_full_tree must be True.
In [65]:
cluster_labels = model.fit_predict(scaled_features)
cluster_labels # each point gets its own label since distance_threshold=0 in the above cell
Out[65]:
array([157, 154, 127,  92, 108,  93, 158, 140, 159, 160, 143, 139, 131,
       141,  94, 163, 111, 106, 125, 120, 138, 115, 161,  90, 156,  69,
       137,  96,  79, 103, 162, 129,  95, 153, 142, 121, 123, 107,  87,
       104, 117,  80, 109, 118, 110, 135, 152, 130, 134, 105, 144, 150,
       147,  70, 166, 124,  51,  71, 136,  99, 126,  54, 151,  75, 155,
        47, 133, 102,  78,  77,  58, 165, 132,  46,  89,  52,  61,  53,
        88,  62, 164,  97,  98,  66, 119,  59, 122, 116, 113,  60,  48,
        76,  67,  81, 149, 101, 112,  25,  68, 128,  83,  57,  33,  64,
        29,  74,  65, 114,  34, 148,  82,  23,  43,  56,  26,  84,  32,
        39,  63,  86,  28, 145,  44,  16,  30,  73, 100, 146,  72,  35,
        49,  85,  91,  38,  40,  45,  19,  55,  37,  18,  31,  41,  14,
        15,  42,  50,  22,  12,  24,  36,  20,  17,  21,  27,  13,   9,
        10,   4,   8,  11,   5,   7,   3,   6,   2,   1,   0], dtype=int64)
In [66]:
from scipy.cluster import hierarchy
linkage_matrix = hierarchy.linkage(model.children_)
linkage_matrix[:][:5] # display only 5 rows
# format: point 1, point 2, distance between the points, number of points in the cluster
Out[66]:
array([[  7.        ,  26.        ,   1.41421356,   2.        ],
       [ 42.        ,  61.        ,   1.41421356,   2.        ],
       [ 48.        , 112.        ,   1.41421356,   2.        ],
       [158.        , 160.        ,   1.41421356,   2.        ],
       [117.        , 142.        ,   1.41421356,   2.        ]])
In [67]:
plt.figure(figsize=(30,10))
hierarchy.set_link_color_palette(['r','grey', 'b', 'grey', 'm', 'grey', 'g', 'grey', 'orange']) # set colors for the clusters
dn = hierarchy.dendrogram(linkage_matrix,truncate_mode='level',p=15, color_threshold=15) # color_threshold=23 sets clusters below y-axis value of 23 to be of the same color
In [68]:
model = AgglomerativeClustering(n_clusters=3) #agglomerative clustering assigning to model variable
In [69]:
cluster_id_hc=model.fit_predict(scaled_features) #fitting and predicting scaled data
In [70]:
model.labels_ #finding labels
Out[70]:
array([2, 1, 1, 2, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 2, 1, 1, 1, 1,
       0, 0, 0, 2, 2, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 2, 2, 0, 2, 0, 0, 0,
       0, 1, 1, 1, 1, 0, 2, 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 1, 1, 2, 2, 1,
       1, 0, 0, 1, 1, 1, 2, 0, 0, 0, 1, 0, 1, 1, 2, 2, 0, 1, 1, 0, 0, 1,
       2, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0, 2, 0, 1, 1, 1, 0, 1, 2, 1, 1, 1,
       0, 0, 2, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 2, 1, 0,
       2, 0, 0, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 2, 1, 2, 2, 1, 1, 0,
       1, 2, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 2], dtype=int64)
In [71]:
country_df_clustered2 = pd.concat([df['country'],df1, pd.DataFrame(cluster_id_hc, columns=['cluster_id_hc'])], axis = 1)
#assigning to country_df_clustered2 variable
In [72]:
country_df_clustered.head() #printing 5 rows of kmeans addded values
Out[72]:
country child_mort exports health imports income inflation life_expec total_fer gdpp cluster_id_km
0 Afghanistan 90.2 55.30 41.9174 248.297 1610 9.44 56.2 5.82 553 2
1 Albania 16.6 1145.20 267.8950 1987.740 9930 4.49 76.3 1.65 4090 1
2 Algeria 27.3 1712.64 185.9820 1400.440 12900 16.10 76.5 2.89 4460 1
3 Angola 119.0 2199.19 100.6050 1514.370 5900 22.40 60.1 6.16 3530 2
4 Antigua and Barbuda 10.3 5551.00 735.6600 7185.800 19100 1.44 76.8 2.13 12200 0
In [73]:
country_df_clustered2.head() #printing 5 rows of hierarchical addded values
Out[73]:
country child_mort exports health imports income inflation life_expec total_fer gdpp cluster_id_hc
0 Afghanistan 90.2 55.30 41.9174 248.297 1610.0 9.44 56.2 5.82 553.0 2
1 Albania 16.6 1145.20 267.8950 1987.740 9930.0 4.49 76.3 1.65 4090.0 1
2 Algeria 27.3 1712.64 185.9820 1400.440 12900.0 16.10 76.5 2.89 4460.0 1
3 Angola 119.0 2199.19 100.6050 1514.370 5900.0 22.40 60.1 6.16 3530.0 2
4 Antigua and Barbuda 10.3 5551.00 735.6600 7185.800 19100.0 1.44 76.8 2.13 12200.0 0
In [74]:
country_df_clustered2=country_df_clustered2.drop(['country','child_mort','exports','health','imports','income','inflation','life_expec','total_fer','gdpp'],axis=1)
In [75]:
df2=pd.DataFrame(country_df_clustered2) #converting to dataframe
In [76]:
df2 #printing df2
Out[76]:
cluster_id_hc
0 2
1 1
2 1
3 2
4 0
... ...
162 1
163 0
164 1
165 2
166 2

167 rows × 1 columns

In [77]:
df #printing df
Out[77]:
country child_mort exports health imports income inflation life_expec total_fer gdpp
0 Afghanistan 90.2 55.30 41.9174 248.297 1610 9.44 56.2 5.82 553
1 Albania 16.6 1145.20 267.8950 1987.740 9930 4.49 76.3 1.65 4090
2 Algeria 27.3 1712.64 185.9820 1400.440 12900 16.10 76.5 2.89 4460
3 Angola 119.0 2199.19 100.6050 1514.370 5900 22.40 60.1 6.16 3530
4 Antigua and Barbuda 10.3 5551.00 735.6600 7185.800 19100 1.44 76.8 2.13 12200
... ... ... ... ... ... ... ... ... ... ...
162 Vanuatu 29.2 1384.02 155.9250 1565.190 2950 2.62 63.0 3.50 2970
163 Venezuela 17.1 3847.50 662.8500 2376.000 16500 45.90 75.4 2.47 13500
164 Vietnam 23.3 943.20 89.6040 1050.620 4490 12.10 73.1 1.95 1310
165 Yemen 56.3 393.00 67.8580 450.640 4480 23.60 67.5 4.67 1310
166 Zambia 83.1 540.20 85.9940 451.140 3280 14.00 52.0 5.40 1460

167 rows × 10 columns

In [78]:
# concatinating the clustering labels with dataframe
country_df_clustered = df.iloc[:,:]
km = pd.concat([df, pd.DataFrame(k_means_labels, columns=['cluster_id_km'])], axis = 1)
country_df_clustered = pd.concat([km, pd.DataFrame(model.labels_, columns=['cluster_id_hc'])], axis = 1)
country_df_clustered.head()
Out[78]:
country child_mort exports health imports income inflation life_expec total_fer gdpp cluster_id_km cluster_id_hc
0 Afghanistan 90.2 55.30 41.9174 248.297 1610 9.44 56.2 5.82 553 2 2
1 Albania 16.6 1145.20 267.8950 1987.740 9930 4.49 76.3 1.65 4090 1 1
2 Algeria 27.3 1712.64 185.9820 1400.440 12900 16.10 76.5 2.89 4460 1 1
3 Angola 119.0 2199.19 100.6050 1514.370 5900 22.40 60.1 6.16 3530 2 2
4 Antigua and Barbuda 10.3 5551.00 735.6600 7185.800 19100 1.44 76.8 2.13 12200 0 0
In [79]:
import plotly.express as px #visualization in 3d format
fig = px.scatter_3d(country_df_clustered, x='country', y='cluster_id_km', z='cluster_id_hc', color=model.fit_predict(scaled_features), opacity=0.75)
fig.update_layout(coloraxis_colorbar=dict(yanchor="top", y=1, x=0, ticks="outside")) 
# fig.update_layout is being used to make the 'color' legend shift towards left side, otherwise the 'color' and 'Gender_Male' legends overlap
# fig.show()
In [80]:
import plotly.express as px #visualization in 3d format
fig = px.scatter_3d(country_df_clustered, x='child_mort', y='exports', z='country', color=model.fit_predict(scaled_features), opacity=0.75)
fig.update_layout(coloraxis_colorbar=dict(yanchor="top", y=1, x=0, ticks="outside")) 
# fig.update_layout is being used to make the 'color' legend shift towards left side, otherwise the 'color' and 'Gender_Male' legends overlap
# fig.show()
In [81]:
# visualising clusters using km, hc values as hue
plt.figure(figsize=(15,5))
plt.subplot(1,3,1)
sns.scatterplot(x = 'gdpp', y = 'child_mort', data= country_df_clustered, hue = 'cluster_id_km', palette="bright")
plt.subplot(1,3,2)
sns.scatterplot(x = 'income', y = 'child_mort', data= country_df_clustered, hue = 'cluster_id_km', palette="bright")
plt.subplot(1,3,3)
sns.scatterplot(x = 'income', y = 'gdpp', data= country_df_clustered, hue = 'cluster_id_hc', palette="bright")
plt.tight_layout()

plt.show()
In [82]:
# sort based on 'child_mort','income','gdpp' in respective order
top5 = country_df_clustered.sort_values(by = ['gdpp','income','child_mort'],
                                                     ascending=[True, True, False]).head(5)
top5 = top5[['country','gdpp','income','child_mort']]
top5 #printing top 5 values of country, income, child_mort columns according to their values
Out[82]:
country gdpp income child_mort
26 Burundi 231 764 93.6
88 Liberia 327 700 89.3
37 Congo, Dem. Rep. 334 609 116.0
112 Niger 348 814 123.0
132 Sierra Leone 399 1220 160.0
In [83]:
# scatter plot for bottom 5 countries based on profiling varibles
plt.figure(figsize=(18, 5))
plt.subplot(1, 3, 1)
sns.scatterplot(x='gdpp', y='child_mort', hue='country',
                data=top5, legend='full', palette="bright", s=300, c='lightblue')
plt.subplot(1, 3, 2)
sns.scatterplot(x='gdpp', y='income', hue='country',
                data=top5, legend='full', palette="bright", s=300, c='lightblue')
plt.subplot(1, 3, 3)
sns.scatterplot(x='income', y='child_mort', hue='country',
                data=top5, legend='full', palette="bright", s=300, c='lightblue')
plt.show() 
#visualising the top5 values using hue as country

DBSCAN¶

In [84]:
from sklearn.cluster import DBSCAN #importin dbscan library

drawing elbow method graph in % between outlier points and epsilon to get the resonable value for epsilon

In [85]:
outlier_percent = [] 

for eps in np.linspace(0.001,3,50): # check 50 values of epsilon between 0.001 and 3
    
    # Create Model
    dbscan = DBSCAN(eps=eps,min_samples=8)
    dbscan.fit(scaled_features)
   
    # Percentage of points that are outliers
    perc_outliers = 100 * np.sum(dbscan.labels_ == -1) / len(dbscan.labels_)
    outlier_percent.append(perc_outliers)
In [86]:
sns.lineplot(x=np.linspace(0.001,3,50),y=outlier_percent, color='red')
plt.ylabel("Percentage of Points Classified as Outliers")
plt.xlabel("Epsilon Value");
#epsilon vs oultiers
In [87]:
dbscan = DBSCAN(eps=1.1,min_samples=8)
dbscan.fit(scaled_features) #fitting scaled data
Out[87]:
DBSCAN(eps=1.1, min_samples=8)
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DBSCAN(eps=1.1, min_samples=8)
In [88]:
dbscan_labels=dbscan.labels_#finding labels using dbscan
In [89]:
dbscan_labels=pd.DataFrame(dbscan_labels)#converting to dataframe
In [90]:
dbscan_labels.value_counts()#checking value counts
Out[90]:
-1    73
 1    56
 0    25
 2    13
dtype: int64
In [91]:
  score = silhouette_score(scaled_features, dbscan_labels)#performing silhouette score

C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\sklearn\utils\validation.py:1111: DataConversionWarning:

A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
In [92]:
score #printing score
Out[92]:
0.12282433720757358
In [93]:
plt.figure(figsize=(10,8))
sns.scatterplot(x=df['exports'], y=df['imports'], hue=dbscan.labels_, palette='viridis'); #visualizing scatter plot
In [94]:
dbscan = DBSCAN(eps=1.1,min_samples=8)
dbscan.fit(X_pca)#fitting pca features into dbscan
Out[94]:
DBSCAN(eps=1.1, min_samples=8)
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DBSCAN(eps=1.1, min_samples=8)
In [95]:
  score = silhouette_score(X_pca, dbscan_labels) #checking silhouette score

C:\Users\MERINA ANGEL\AppData\Local\Programs\Python\Python310\lib\site-packages\sklearn\utils\validation.py:1111: DataConversionWarning:

A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
In [96]:
score
Out[96]:
0.09515643255791717
In [97]:
plt.figure(figsize=(10,8))
sns.scatterplot(x='PC1', y='PC2',data=X_pca, hue=dbscan.labels_, palette='viridis');#visualizing scatter plot
In [ ]:
In [98]:
from sklearn.neighbors import NearestNeighbors
neighbors = NearestNeighbors(n_neighbors=20)
neighbors_fit = neighbors.fit(scaled_features)
distances, indices = neighbors_fit.kneighbors(scaled_features) #using nneighbours we will know the nearest values
In [99]:
distances = np.sort(distances, axis=0)
distances = distances[:,1]
plt.plot(distances)
plt.grid()
#Lets plot the distances of each point in ascending order of the distance, elbow point will give us the samller range for optimal eps value.
In [100]:
min_samples = range(10,20)
eps = np.arange(1.2,2.0,0.1) # returns array of ranging from 1.0 to 1.5 with step of 0.1
In [101]:
output = []

for ms in min_samples:
    for ep in eps:
        labels = DBSCAN(min_samples=ms, eps = ep).fit(X_pca).labels_
        print(labels)
        score = silhouette_score(X_pca, labels)
        output.append((ms, ep, score))
        #values of output were printed using append()

[ 0  0  0 -1  0 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1  0 -1
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In [102]:
min_samples, eps, score = sorted(output, key=lambda x:x[-1])[-1]
print(f"Best silhouette_score: {score}")
print(f"min_samples: {min_samples}")
print(f"eps: {eps}") #Get the parameters for best silhouette score

Best silhouette_score: 0.38111320835438417
min_samples: 19
eps: 1.9000000000000006
In [103]:
from collections import Counter
In [104]:
labels = DBSCAN(min_samples=19, eps = 1.9).fit(X_pca).labels_
clusters = len(Counter(labels))
print(f"Number of clusters: {clusters}")
print(f"Number of outliers: {Counter(labels)[-1]}")
print(f"Silhouette_score: {silhouette_score(X_pca, labels)}")

Number of clusters: 2
Number of outliers: 2
Silhouette_score: 0.38111320835438417
In [105]:
plt.figure(figsize=(10,8))
sns.scatterplot(x=df['child_mort'], y=df['imports'], hue=labels, palette='viridis');
In [ ]:
In [106]:
#cluster formation based on country 
print("Cluster 0 of K_means Clustering model : ")
print(country_df_clustered[country_df_clustered['cluster_id_km'] == 0].country.unique())
print('\n')

print("Cluster 1 of K_means Clustering model : ")
print(country_df_clustered[country_df_clustered['cluster_id_km'] == 1].country.unique())
print('\n')


print("Cluster 2 of K_means Clustering model : ")
print(country_df_clustered[country_df_clustered['cluster_id_km'] == 2].country.unique())
print('\n')

Cluster 0 of K_means Clustering model : 
['Antigua and Barbuda' 'Australia' 'Austria' 'Bahamas' 'Bahrain'
 'Barbados' 'Belgium' 'Brunei' 'Canada' 'Chile' 'Croatia' 'Cyprus'
 'Czech Republic' 'Denmark' 'Equatorial Guinea' 'Estonia' 'Finland'
 'France' 'Germany' 'Greece' 'Hungary' 'Iceland' 'Ireland' 'Israel'
 'Italy' 'Japan' 'Kuwait' 'Latvia' 'Libya' 'Lithuania' 'Luxembourg'
 'Malaysia' 'Malta' 'Netherlands' 'New Zealand' 'Norway' 'Oman' 'Poland'
 'Portugal' 'Qatar' 'Saudi Arabia' 'Seychelles' 'Singapore'
 'Slovak Republic' 'Slovenia' 'South Korea' 'Spain' 'Sweden' 'Switzerland'
 'United Arab Emirates' 'United Kingdom' 'United States']


Cluster 1 of K_means Clustering model : 
['Albania' 'Algeria' 'Argentina' 'Armenia' 'Azerbaijan' 'Bangladesh'
 'Belarus' 'Belize' 'Bhutan' 'Bolivia' 'Bosnia and Herzegovina' 'Botswana'
 'Brazil' 'Bulgaria' 'Cambodia' 'Cape Verde' 'China' 'Colombia'
 'Costa Rica' 'Dominican Republic' 'Ecuador' 'Egypt' 'El Salvador' 'Fiji'
 'Georgia' 'Grenada' 'Guatemala' 'Guyana' 'Haiti' 'India' 'Indonesia'
 'Iran' 'Iraq' 'Jamaica' 'Jordan' 'Kazakhstan' 'Kyrgyz Republic' 'Lebanon'
 'Macedonia, FYR' 'Maldives' 'Mauritius' 'Micronesia, Fed. Sts.' 'Moldova'
 'Mongolia' 'Montenegro' 'Morocco' 'Myanmar' 'Nepal' 'Panama' 'Paraguay'
 'Peru' 'Philippines' 'Romania' 'Russia' 'Samoa' 'Serbia' 'South Africa'
 'Sri Lanka' 'St. Vincent and the Grenadines' 'Suriname' 'Tajikistan'
 'Thailand' 'Tonga' 'Tunisia' 'Turkey' 'Turkmenistan' 'Ukraine' 'Uruguay'
 'Uzbekistan' 'Vanuatu' 'Venezuela' 'Vietnam']


Cluster 2 of K_means Clustering model : 
['Afghanistan' 'Angola' 'Benin' 'Burkina Faso' 'Burundi' 'Cameroon'
 'Central African Republic' 'Chad' 'Comoros' 'Congo, Dem. Rep.'
 'Congo, Rep.' "Cote d'Ivoire" 'Eritrea' 'Gabon' 'Gambia' 'Ghana' 'Guinea'
 'Guinea-Bissau' 'Kenya' 'Kiribati' 'Lao' 'Lesotho' 'Liberia' 'Madagascar'
 'Malawi' 'Mali' 'Mauritania' 'Mozambique' 'Namibia' 'Niger' 'Nigeria'
 'Pakistan' 'Rwanda' 'Senegal' 'Sierra Leone' 'Solomon Islands' 'Sudan'
 'Tanzania' 'Timor-Leste' 'Togo' 'Uganda' 'Yemen' 'Zambia']
In [107]:
#cluster formation based on country 
print("Cluster 0 of hierarchical Clustering model : ")
print(country_df_clustered[country_df_clustered['cluster_id_hc'] == 0].country.unique())
print('\n')

print("Cluster 1 of hierarchical Clustering model : ")
print(country_df_clustered[country_df_clustered['cluster_id_hc'] == 1].country.unique())
print('\n')


print("Cluster 2 of hierarchical Clustering model : ")
print(country_df_clustered[country_df_clustered['cluster_id_hc'] == 2].country.unique())
print('\n')

Cluster 0 of hierarchical Clustering model : 
['Antigua and Barbuda' 'Australia' 'Austria' 'Bahamas' 'Bahrain'
 'Barbados' 'Belgium' 'Brazil' 'Brunei' 'Bulgaria' 'Canada' 'Chile'
 'Costa Rica' 'Croatia' 'Cyprus' 'Czech Republic' 'Denmark'
 'Equatorial Guinea' 'Estonia' 'Finland' 'France' 'Germany' 'Greece'
 'Hungary' 'Iceland' 'Ireland' 'Israel' 'Italy' 'Japan' 'Kuwait' 'Latvia'
 'Lebanon' 'Libya' 'Lithuania' 'Luxembourg' 'Malaysia' 'Maldives' 'Malta'
 'Mauritius' 'Montenegro' 'Netherlands' 'New Zealand' 'Norway' 'Oman'
 'Panama' 'Poland' 'Portugal' 'Qatar' 'Romania' 'Saudi Arabia'
 'Seychelles' 'Singapore' 'Slovak Republic' 'Slovenia' 'South Korea'
 'Spain' 'Sweden' 'Switzerland' 'Turkey' 'United Arab Emirates'
 'United Kingdom' 'United States' 'Uruguay' 'Venezuela']


Cluster 1 of hierarchical Clustering model : 
['Albania' 'Algeria' 'Argentina' 'Armenia' 'Azerbaijan' 'Bangladesh'
 'Belarus' 'Belize' 'Bhutan' 'Bolivia' 'Bosnia and Herzegovina' 'Botswana'
 'Cambodia' 'Cape Verde' 'Central African Republic' 'China' 'Colombia'
 'Dominican Republic' 'Ecuador' 'Egypt' 'El Salvador' 'Fiji' 'Georgia'
 'Grenada' 'Guatemala' 'Guyana' 'Haiti' 'India' 'Indonesia' 'Iran'
 'Jamaica' 'Jordan' 'Kazakhstan' 'Kyrgyz Republic' 'Lao' 'Lesotho'
 'Macedonia, FYR' 'Micronesia, Fed. Sts.' 'Moldova' 'Mongolia' 'Morocco'
 'Myanmar' 'Namibia' 'Nepal' 'Pakistan' 'Paraguay' 'Peru' 'Philippines'
 'Russia' 'Samoa' 'Serbia' 'Solomon Islands' 'South Africa' 'Sri Lanka'
 'St. Vincent and the Grenadines' 'Suriname' 'Tajikistan' 'Thailand'
 'Tonga' 'Tunisia' 'Turkmenistan' 'Ukraine' 'Uzbekistan' 'Vanuatu'
 'Vietnam']


Cluster 2 of hierarchical Clustering model : 
['Afghanistan' 'Angola' 'Benin' 'Burkina Faso' 'Burundi' 'Cameroon' 'Chad'
 'Comoros' 'Congo, Dem. Rep.' 'Congo, Rep.' "Cote d'Ivoire" 'Eritrea'
 'Gabon' 'Gambia' 'Ghana' 'Guinea' 'Guinea-Bissau' 'Iraq' 'Kenya'
 'Kiribati' 'Liberia' 'Madagascar' 'Malawi' 'Mali' 'Mauritania'
 'Mozambique' 'Niger' 'Nigeria' 'Rwanda' 'Senegal' 'Sierra Leone' 'Sudan'
 'Tanzania' 'Timor-Leste' 'Togo' 'Uganda' 'Yemen' 'Zambia']
In [108]:
country_df_clustered
Out[108]:
country child_mort exports health imports income inflation life_expec total_fer gdpp cluster_id_km cluster_id_hc
0 Afghanistan 90.2 55.30 41.9174 248.297 1610 9.44 56.2 5.82 553 2 2
1 Albania 16.6 1145.20 267.8950 1987.740 9930 4.49 76.3 1.65 4090 1 1
2 Algeria 27.3 1712.64 185.9820 1400.440 12900 16.10 76.5 2.89 4460 1 1
3 Angola 119.0 2199.19 100.6050 1514.370 5900 22.40 60.1 6.16 3530 2 2
4 Antigua and Barbuda 10.3 5551.00 735.6600 7185.800 19100 1.44 76.8 2.13 12200 0 0
... ... ... ... ... ... ... ... ... ... ... ... ...
162 Vanuatu 29.2 1384.02 155.9250 1565.190 2950 2.62 63.0 3.50 2970 1 1
163 Venezuela 17.1 3847.50 662.8500 2376.000 16500 45.90 75.4 2.47 13500 1 0
164 Vietnam 23.3 943.20 89.6040 1050.620 4490 12.10 73.1 1.95 1310 1 1
165 Yemen 56.3 393.00 67.8580 450.640 4480 23.60 67.5 4.67 1310 2 2
166 Zambia 83.1 540.20 85.9940 451.140 3280 14.00 52.0 5.40 1460 2 2

167 rows × 12 columns

This are the clusters formed for countries with the help of pca, kmeans,hierarchical.¶

They are :-(AS PER CLUSTERING REPRESENTATION)

under-Developed countries  (CLUSTER 2),

Developing countries (CLUSTER 1),  

developed countries (CLUSTER 0)

Conclusions:¶

  1. Here, according to less child_mort rate, high gdpp we can say 1st CLUSTER (i.e cluster 0) as a developed countries.
  1. Remaining 2nd CLUSTER is considered as developing country (i.e cluster 1)
  1. With less gdpp, high child_mort rate compared to other countries are considered as 3rd CLUSTER (i.e cluster 2) represented as under developed countries and this countries require help from international humanitarian NGO

cluster 2 are the under developed countries require help from international humanitarian NGO.

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